Improvements in or relating to the measurement of current within a conductor

ABSTRACT

In the field of Rogowski coils for the measurement of current within a conductor there is provided an electrical interface for connection to a Rogowski coil arranged around a primary conductor. The electrical interface includes an input that is configured to sample an input voltage signal from the Rogowski coil. The electrical interface also has an integrator circuit which includes an integrator module that is configured to integrate the sampled input voltage signal to provide an output voltage signal from which can be derived a primary current flowing through the primary conductor. The integrator module employs a transfer function that includes an attenuation factor.

This invention relates to an electrical interface for connection to aRogowski coil that is arranged around a primary conductor.

A Rogowski coil 10 is an electrical device for measuring alternatingcurrent (AC). As shown in FIG. 1, it consists of a helical coil 12 ofwire 14 which is wrapped around a primary conductor 16 whose current,i.e. primary current i_(p), is to be measured. The coil 12 is mutuallycoupled with the primary conductor 16 via air, and so the absence of aniron core means that no saturation of the coil 12 will occur,irrespective of the level of current flowing through the primaryconductor 16.

The voltage induced in the coil 12 is proportional to the rate ofchange, i.e. the derivative, of the primary current i_(p) flowingthrough the primary conductor 16. The output of the Rogowski coil 10 cantherefore be connected to an electrical or electronic integrator toprovide an output signal that is proportional to the primary currenti_(p).

According to an aspect of the invention there is provided an electricalinterface, for connection to a Rogowski coil arranged around a primaryconductor, including:

-   -   an input configured to sample an input voltage signal from the        Rogowski coil; and    -   an integrator circuit including an integrator module configured        to integrate the sampled input voltage signal to provide an        output voltage signal from which can be derived a primary        current flowing through the primary conductor, the integrator        module employing a transfer function that includes an        attenuation factor.

The inclusion within the integrator circuit of an integrator modulewhich employs a transfer function that includes an attenuation factordesirably maintains stability of the operation of the integrator modulewithout unduly impacting on its accuracy, particularly at very highsampling frequencies, e.g. many tens of thousands of samples per second.

Preferably the attenuation factor gives rise to an error in the derivedprimary current flowing through the primary conductor that is notgreater than a predetermined percentage selected according to the natureof the primary current (i_(p)) flowing through the primary conductor(16).

The percentage error in the derived primary current (i_(p)(n)) may beselected to be:

-   -   not greater than 10% when the primary current (i_(p)) is        decaying; and    -   not greater than 0.3% when the primary current (i_(p)) is in        steady state.

Such features advantageously limit the size of the attenuation factor toa level which provides for an acceptable overall degree of accuracy forthe integrator circuit, particularly at very high sampling frequencies(i.e. typically many thousands of samples per second), withoutsacrificing the stability of operation of the integrator module therein.

Optionally the integrator module employs a transfer function whichadditionally down-samples a previous output voltage signal.

Down-sampling only a previous output voltage signal, i.e. a feedbackoutput voltage signal, helps to reduce distortion in a subsequent outputvoltage signal (which might otherwise arise because of the integratormodule becoming saturated) without affecting the sampling frequency atwhich the input operates, which as indicated above may be many tens ofthousands of samples per second.

The integrator module may be or include one or more of:

-   -   a first rectangular integrator embodying a transfer function in        the discrete time domain of the form

${{H(z)} = \frac{1}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}}};$

-   -   a second rectangular integrator embodying a transfer function in        the discrete time domain of the form

${{H(z)} = {\frac{1}{N_{d}}\frac{\sum\limits_{k = 0}^{N_{d}}z^{- k}}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}}}};$

-   -   a trapezoidal integrator embodying a transfer function in the        discrete time domain of the form

${{H(z)} = {\frac{1}{N_{d}}\frac{{\sum\limits_{k = 0}^{N_{d}}z^{- k}} - \frac{1}{2} - {\frac{1}{2}z^{- N_{d}}}}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}}}};$

and

-   -   a Taylor's approximation integrator embodying a transfer        function in the discrete time domain of the form

${{H(z)} = {\frac{1}{6}\left\{ \frac{1 + {4z^{{- N_{d}}/2}} + z^{- N_{d}}}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}} \right\}}},$

where,

-   -   A is the attenuation factor;    -   T_(s) is a sampling period of the input voltage signal; and    -   N_(d) is a down-sampling scale.

Each of the foregoing integrators provides a desired degree of accuracy,particularly at high sampling frequencies, e.g. typically of manythousands per second, while maintaining their operational stability.

In a preferred embodiment of the invention the integrator circuitadditionally includes at least one averaging module arranged incommunication with the output of the integrator module, the or eachaveraging module being configured to calculate an average output voltagesignal over one or more operating cycles of an electrical system ofwhich the primary conductor forms a part and to subtract the saidcalculated average output voltage from the output voltage signalprovided by the integrator module to establish a corrected outputvoltage signal.

The inclusion of one or more such averaging modules removes lowfrequency noise from the output voltage signal provided by theintegrator module as well as any inherent DC voltage offset in the inputvoltage signal when sampling begins.

In another preferred embodiment of the invention the integrator circuitfurther includes a disturbance detector configured to detect adisturbance in the current flowing through the primary conductor andthereafter suspend operation of the or each averaging module while thedisturbance remains.

The inclusion of a disturbance detector, and more particularlysuspending operation of the or each averaging module if there is adisturbance in the primary conductor, helps to ensure that the previousoutput voltage signal from the integrator module is maintained and sothe accuracy with which any DC voltage offset is removed from the outputvoltage signal is unaffected by the disturbance and so is similarlymaintained.

Optionally the disturbance detector is configured to determine theabsolute value of the sampled input voltage signal and to detect adisturbance in the current flowing through the primary conductor whenthe absolute value of the sampled input voltage signal exceeds apredetermined threshold.

Such an arrangement readily and reliably implements the detection of arise in the current flowing in the primary conductor, and hencefacilitates the desired detection of a disturbance in the primaryconductor.

Preferably the integrator circuit still further includes areconstruction module which is configured to derive the primary currentflowing through the primary conductor by multiplying the correctedoutput voltage signal by a gain factor.

The inclusion of such a reconstruction module desirably permits theintegrator circuit to output a primary current value corresponding tothe level of current flowing through the primary conductor that can beused, e.g. in other control or monitoring operations associated with theprimary conductor.

The reconstruction module may also be configured to modify the correctedoutput voltage signal to compensate for errors arising from theattenuation factor.

Optionally the reconstruction module carries out one or more of phasecompensation and steady state input signal compensation.

The foregoing features advantageously help to further maintain theaccuracy of the derived primary current.

In a still further preferred embodiment of the invention thereconstruction module is also configured to modify the gain factoraccording to a measured temperature of the electrical interface.

Such a reconstruction module usefully helps the integrator circuit toindicate actual changes in the derived primary current which mightotherwise be masked by temperature changes in or adjacent to theelectrical interface.

There now follows a brief description of preferred embodiments of theinvention, by way of non-limiting example, with reference being made tothe following figures in which:

FIG. 1 shows a schematic view of a conventional Rogowski coil arrangedaround a primary conductor; and

FIG. 2 shows a schematic view of an electrical interface according to anembodiment of the invention.

An electrical interface according to a first embodiment of the inventionis designated generally by reference numeral 30, as shown in FIG. 2.

The electrical interface 30 includes an input 32 which is configured tosample an input voltage signal u_(s)(n) from a Rogowski coil 10 that isarranged around a primary conductor 16.

The input 32 operates at a very high sampling frequency, which istypically many tens of thousands of samples per second and may, forexample, be 64,800 Hz which gives a sampling period T_(s) of 1/64800seconds, i.e. 0.0000155 seconds.

The electrical interface 30 also includes an integrator circuit 34which, in turn, includes an integrator module 36 that in the embodimentshown is a digital integrator module 36, i.e. is an integrator modulewhich operates in the discrete time, or digital domain.

The integrator module 36 is configured to integrate the sampled inputvoltage signal u_(s)(n) to provide an output signal u_(INT)(n) fromwhich can be derived the primary current i_(p)(n) flowing through aprimary conductor 16 around which an associated Rogowski coil 10 is, inuse, arranged.

The integrator module 36 employs a transfer function that includes anattenuation factor A. The attenuation factor A is chosen such that theerror in the derived primary current i_(p)(n) flowing through theprimary conductor 16 is not greater than a predetermined percentagewhich is selected according to the nature of the primary current i_(p)flowing through the primary conductor 16.

For example, in circumstances when the primary current i_(p) is decayingthen the percentage error is selected to be not more than 10%. When theprimary current i_(p) is in steady state, i.e. neither increasing nordecreasing, then the percentage error in the derived primary currenti_(p)(n) is selected to be not more than 0.3%.

The integrator module 36 also employs a transfer function whichadditionally down-samples a previous output voltage signal u_(INT)(n),i.e. a feedback output voltage signal as part of its operation.

More particularly, in the embodiment shown the integrator module 36adopts a rectangular approximation of the required integration as setout in the following frequency expression:

u _(INT)(n)=K _(I) u _(INT)(n−N _(d))+u _(s)(n)

where,

-   -   u_(INT)(n) is the output voltage signal generated by the        integrator module 36;    -   u_(s)(n) is the sampled input voltage signal from the associated        Rogowski coil 10;    -   N_(d) is the down-sampling scale which, by way of example, is        16;    -   T_(s) is the sampling period of the input voltage signal        u_(s)(n) which, for an exemplary sampling frequency of 64,800 Hz        is given by 1/64,8006, i.e. 0.00000155 seconds; and    -   K_(I) is given by

K _(I) =e ^(−AN) ^(d) ^(T) ^(s)

with,

A being the attenuation factor which, by way of example, is 0.5.

Other values for the down-sampling scale N_(d), sampling period T_(s),and attenuation factor A, may be used in other embodiments of theinvention.

In view of the above-mentioned frequency expression, the integratormodule 36 can be said to define a rectangular integrator that embodies atransfer function in the discrete time domain of the form

${H(z)} = \frac{1}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}}$

Accordingly, utilising the example values indicated above, the maximumoutput of the transfer function will be

$\frac{1}{1 - e^{{- 0.5}*16*0.0000155}} = {8,100}$

This compares to a maximum output of 129,600 for a conventionalintegrator which omits both an attenuation factor and the down-samplingof a previous output voltage signal. Such a large potential maximumoutput, which is an order of magnitude greater than that achieved by thefirst embodiment of the invention, means that the conventionalintegrator will very quickly magnify any error in the sampled inputvoltage signal, particularly at very high sampling frequencies (i.e.many tens of thousands of samples per second), and will therefore becomesaturated. As a consequence the accuracy of the output of such aconventional integrator is also lost.

In the meantime, an attenuation factor of 0.5 means that a DC offset inthe sampled input voltage signal u_(s)(n) with a decaying time constantof 275 milliseconds results in an error in the derived primary currenti_(p)(n) that is less than 10%.

In other embodiments of the invention (not shown) the integrator module36 may adopt a more accurate trapezoidal approximation of the requiredintegration, e.g. as set out in the following frequency expression:

${u_{INT}(n)} = {{K_{I}{u_{INT}\left( {n - N_{d}} \right)}} + {\left\{ {\frac{u_{s}(n)}{2} + \frac{u_{s}\left( {n - N_{d}} \right)}{2} + {\sum\limits_{k = {n - N_{d}}}^{n}{u_{s}(k)}}} \right\}/N_{d}}}$

Such an integrator module 36 therefore defines a trapezoidal integratorwhich embodies a transfer function in the discrete time domain of theform

${H(z)} = {\frac{1}{N_{d}}\frac{{\sum\limits_{k = 0}^{N_{d}}z^{- k}} - \frac{1}{2} - {\frac{1}{2}z^{- N_{d}}}}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}}}$

The integrator module 36 may also adopt a Taylor's approximation of therequired integration, e.g. as set out in the following frequencyexpression:

u _(INT)(n)=K _(I) u _(INT)(n−N _(d))+{u _(s)(n)+4u _(s)(n−N _(d)/2)+u_(s)(n−N _(d))}/6

Such an integrator module 36 therefore defines a Taylor's approximationintegrator which embodies a transfer function in the discrete timedomain of the form

${H(z)} = {\frac{1}{6}\left\{ \frac{1 + {4z^{{- N_{d}}/2}} + z^{- N_{d}}}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}} \right\}}$

In still further embodiments of the invention the integrator modulecould define a second rectangular integrator (which is more accuratethan the first rectangular integrator mentioned hereinabove) thatembodies a transfer function in the discrete time domain of the form

${H(z)} = {\frac{1}{N_{d}}\frac{\sum\limits_{k = 0}^{N_{d}}z^{- k}}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}}}$

Returning to the embodiment shown in FIG. 2, the integrator circuit 34also includes first and second averaging modules 38, 40. The firstaveraging module 38 is arranged in direct communication with the outputof the integrator module 36, and the second averaging module 40 isarranged in communication with the integrator module 36 via the firstaveraging module 38.

Each averaging module 38, 40 is configured to calculate an averageoutput voltage signal over one operating cycle of an electrical systemof which the primary conductor 16 forms a part, and to subtract thecalculated average output voltage from the output voltage signalu_(INT)(n) provided by the integrator module 36 to establish a correctedoutput voltage signal u_(pp)(n).

More particularly, the first averaging module 38 subtracts thecalculated average output voltage directly from the output voltagesignal u_(INT)(n) provided by the integrator module 36 and the secondaveraging module 40 subtracts the calculated average voltage from themodified output of the first averaging module 38 to establish thecorrected output voltage signal u_(pp)(n).

In other embodiments of the invention the integrator circuit may includefewer than or more than two series-connected averaging modules. One ormore of the averaging modules may also calculate an average outputvoltage over more than one operating cycle of the electrical system ofwhich the primary conductor forms a part.

By way of example one or more of the averaging modules 38, 40 may employa first method of calculating the average output voltage according to

${y(n)} = {\frac{1}{N}{\sum\limits_{k = {n - N + 1}}^{n}{x(k)}}}$

where,

-   -   y(n) is the calculated average voltage; and

N is the number of samples per cycle of fundamental frequency f₀ of theelectrical system of which the primary conductor 16 forms a part, with Nbeing given by

$N = \frac{1}{T_{s} \times f_{0}}$

which, using the example values set out above and a fundamentalfrequency f₀ of 50 Hz, gives

$\begin{matrix}{\; {= \frac{64800}{50}}} \\{= 1296}\end{matrix}$

One or more of the averaging modules 38, 40 may also employ a secondmethod of calculating the average output voltage according to

${y(n)} = {{y\left( {n - 1} \right)} + \frac{x(n)}{N} - \frac{x\left( {n - N} \right)}{N}}$

where N is again given by

$N = \frac{1}{T_{s} \times f_{0}}$

One or more of the averaging modules 38, 40 might still further employ athird method of calculating the average output voltage according to

${y(n)} = \frac{{h(n)} - {h\left( {n - N} \right)}}{N}$

where,

-   -   h(n)=h(n−1)+x(n); and    -   N is given by

$\begin{matrix}{N = \frac{1}{T_{s} \times f_{0}}} \\{= 1296}\end{matrix}$

In addition to the foregoing the integrator circuit 34 also includes adisturbance detector 42 that is configured to detect a disturbance inthe current flowing through the primary conductor 16 and thereaftersuspend operation of the first and second averaging modules 38, 40 whilethe disturbance remains.

Such suspension of the operation of the first and second averagingmodules 38, 40 means that neither subtracts the calculated averagevoltage signal from the output voltage signal u_(INT)(n) generated bythe integrator module 36, and so the extent to which any DC voltageoffset is removed from the output voltage signal u_(INT)(n) is frozen,and thereby is unaffected by the disturbance.

The disturbance detector 42 detects a disturbance in the current flowingthrough the primary conductor 16 by determining the absolute value ofthe sampled input voltage signal u_(s)(n), e.g. the maximum absolutevalue of the sampled input voltage signal u_(s)(n) over the previousoperating cycle of the electrical system of which the primary conductor16 forms a part, and establishing that a rise in current has occurred(which is indicative of there being a disturbance in the current flowingin the primary conductor 16) when the absolute value of the sample inputvoltage exceeds a predetermined threshold.

The integrator circuit 34 also includes a reconstruction module 44 whichis configured to derive the primary current i_(p)(n) flowing in theprimary conductor 16 by multiplying the corrected output voltage signalu_(pp)(n), i.e. as output by the second averaging module 40, by a gainfactor K_(L)(T_(c)).

The reconstruction module 44 also, first of all, modifies the correctedoutput voltage u_(pp)(n) to compensate for errors arising from theattenuation factor A.

More particularly, the reconstruction module 44 carries out phasecompensation N_(comp) and steady state input signal compensationA_(comp) to produce a modified corrected output voltage signal i_(pp)(n)according to

i _(PP)(n)=A _(comp) u _(PP)(n−N _(comp))

where,

-   -   N_(comp) is the number of samples for phase compensation and is        given by

${N_{comp} = {{floor}\left( \frac{{\pi/2} - {\arctan \left( {\omega_{0}/A} \right)}}{\omega_{0}T_{s}} \right)}};$

and

-   -   A_(comp) is the compensation value for the steady state input        signal which is given by

$A_{comp} = {N_{d}\omega_{0}T_{s}\sqrt{1 + \left( \frac{A}{\omega_{0}} \right)^{2}}}$

with,

-   -   ω₀ being the angular frequency of the associated electrical        system of which the primary conductor 16 is a part, which is        given by ω₀=2πf ₀ (with f₀ being the fundamental frequency of        the associated electrical system which, as given above by way of        example is 50 Hz, but might also be 60 Hz).

Thereafter the reconstruction module 44 derives the primary currenti_(p)(n) flowing in the primary conductor 16 by multiplying the modifiedcorrected output voltage signal i_(pp)(n) according to the following

i _(P)(n)=K _(L)(T _(c))i _(PP)(n)

where,

-   -   K_(L) (T_(c)) is the gain factor which is given by

K _(L)(T _(c))=K ₀+α(T−T ₀)+β(T−T ₀)²

with,

-   -   K₀ being 1/L_(Rogow) which is a characteristic of the Rogowski        coil 10 that is determined under laboratory conditions at a        standard temperature T₀ of 20° C.;    -   α and β being temperature dependent coefficients; and        -   T being a measured temperature of the electrical interface            30.

What we claim is:
 1. An electrical interface, for connection to aRogowski coil arranged around a primary conductor, comprising: an inputconfigured to sample an input voltage signal from the Rogowski coil; andan integrator circuit including an integrator module configured tointegrate the sampled input voltage signal to provide an output voltagesignal from which can be derived a primary current flowing through theprimary conductor, the integrator module employing a transfer functionthat includes an attenuation factor.
 2. The electrical interfaceaccording to claim 1, wherein the attention factor gives rise to anerror in the derived primary current flowing through the primaryconductor that is not greater than a predetermined percentage selectedaccording to the nature of the primary current flowing through theprimary conductor.
 3. The electrical interface according to claim 2,wherein the percentage error in the derived primary current is selectedto be: not greater than 10% when the primary current is decaying; andnot greater than 0.3% when the primary current is in steady state. 4.The electrical interface according to any preceding claim 1, wherein theintegrator module employs a transfer function which additionallydown-samples a previous output voltage signal.
 5. The electricalinterface according to claim 1, wherein the integrator module is orincludes one or more of: a first rectangular integrator embodying atransfer function in the discrete time domain of the form${{H(z)} = \frac{1}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}}};$ asecond rectangular integrator embodying a transfer function in thediscrete time domain of the form${{H(z)} = {\frac{1}{N_{d}}\frac{\sum\limits_{k = 0}^{N_{d}}z^{- k}}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}}}};$a trapezoidal integrator embodying a transfer function in the discretetime domain of the form${{H(z)} = {\frac{1}{N_{d}}\frac{{\sum\limits_{k = 0}^{N_{d}}z^{- k}} - \frac{1}{2} - {\frac{1}{2}z^{- N_{d}}}}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}}}};$and a Taylor's approximation integrator embodying a transfer function inthe discrete time domain of the form${{H(z)} = {\frac{1}{6}\left\{ \frac{1 + {4z^{{- N_{d}}/2}} + z^{- N_{d}}}{1 - {e^{{- {AT}_{s}}N_{d}}z^{- N_{d}}}} \right\}}},$where, A is the attenuation factor; Ts is a sampling period of the inputvoltage signal; and Nd is a down-sampling scale.
 6. The electricalinterface according to claim 1, wherein the integrator circuitadditionally includes at least one averaging module arranged incommunication with the output of the integrator module, the or eachaveraging module being configured to calculate an average output voltagesignal over one or more operating cycles of an electrical system ofwhich the primary conductor forms a part and to subtract the saidcalculated average output voltage from the output voltage signalprovided by the integrator module to establish a corrected outputvoltage signal.
 7. The electrical interface according to claim 6,wherein the integrator circuit further includes a disturbance detectorconfigured to detect a rise in current flowing through the primaryconductor and thereafter suspend operation of the or each averagingmodule while the disturbance remains.
 8. The electrical interfaceaccording to claim 7, wherein the disturbance detector is configured todetermine the absolute value of the sampled input voltage signal and todetect a rise in current flowing through the primary conductor when theabsolute value of the sampled input voltage signal exceeds apredetermined threshold.
 9. The electrical interface according to claim6, wherein the integrator circuit still further includes areconstruction module which is configured to derive the primary currentflowing through the primary conductor by multiplying the correctedoutput voltage signal by a gain factor.
 10. The electrical interfaceaccording to claim 9, wherein the reconstruction module is alsoconfigured to modify the corrected output voltage signal to compensatefor errors arising from the attenuation factor.
 11. The electricalinterface according to claim 10, wherein the reconstruction modulecarries out one or more of phase compensation and steady state inputsignal compensation.
 12. The electrical interface according to claim 9,wherein the reconstruction module is also configured to modify the gainfactor according to a measured temperature of the electrical interface.